Class Project

I am currently a graduate student in computational math and we are required to do a CFD project? The length of time of this project is only a semester. Does anybody have any ideas for projects? Please let me know, thank you.

How about a phase-field simulation of dendritic growth with coupled bouyancy induced natural convection. Refer to the Ivanstov theory for self similarity. Model CS as a paraboloid of revolution. Seems like a neat problem.

Depends on what they want you to learn from the project. If they want you to learn about the physics, then do something involving turbulence models. If they want you to learn about numerical methods, do something about compressible flows and the variations you get with different descritisation methods. You could do a nice supersonic jet, and run it with lots of different solution schemes, and compare the apparent numerical diffusion/Gibbs errors etc. Or, if you want to be really clever, you could have a moving reference frame mesh with some sort of closed loop control (like on an aircraft). That would be GREAT! Or you could just prove that numerical diffusion is worse when the flow is diagonal to grid lines. Or just write about the conjugate gradiant method.

...or maybe you could come up with an UBER higher order scheme, or write a paper explaining to us poor engineering types what things like monotonicity and TVD actually mean (something to do with boundedness apparently). Or maybe you could derive the Navier-Stokes equations from scratch. I knew a maths guy who did that once. You maths types like those sorts of pointless exercises don't you. How about writing a little CFD solver that uses the finite element method instead of the finite volume, and have it working with solid mechanics, then I wouldn't have to use CFX anymore to do my aeroelastics. Or maybe you could invent a new sort of cell, that has all the flexibility of tets, but with the low diffusion of hexas. Or write a surface tension algorithm that actually works. Or debug PHOENICS so that actually works. Or you could write about Fourier analysis of residual plots. And then you can explain it to me.